Ceiling – How to properly double on ceiling joists

Presuming this is the area from How two install hardwood floors in a long room with a subfloor that has a plane change in the middle? It really should be rot from being unprotected against the moist brick, which looks the same as termite damage...unless you found dead or live termites of course. Future instances can be avoided with just a Zip-lock type freezer bag over the beam's end.

But, No on the anchor idea, just not strong nor uniform enough. And No, on the iLikeDirt idea, it separates the floor from the structure. If you can't just shim them & leave sleeping dogs lie. Then, get a carpenter to get their thoughts on threat level of leaving them & what's proper &/or legal in your area for a repair.

Now, if you're lucky see if you have slots instead of pockets, this you can work with to get new beams in. Meaning, can you see the full pocket & a subfloor gap or does the subfloor seem to go into the brick?

If no, then one very successful (& proper & legal around me) method is to put or leave full depth scabs in the pockets.

And, those get end-lagged into & through your new ledger, which is actually a whole new floor frame.

Just to kind of give you another view of the practice of framing in a new floor structure with old &/or new lumber. It looks something like this with the scabs being on the backside of the ledger or the light wood (it's a bad & wrong picture, but the best basic visual I could find).

You would supplement the lags with upside down joist hangers on top of the scabs, since lags don't have the full shear resistance of a 2x8. Again, just for your visual understanding if the carpenter starts explaining what he'd do & it happens to sound like this. Or, see what he thinks of this, him falling down laughing would be explanation enough.

The benefits of the above method is that nothing changes, the pockets keep doing what they've done, the structure remains braced, no damage is done to any brick in trying to coax new beams in that may be too long & outwardly stress the structure & the new ledgers & joists can be custom heighted. But, hopefully the carpenter's just fine with leaving them in.

Blown in cellulose can be quite effective if all air gaps are located and sealed with expanding foam for this purpose. Look for gaps around light boxes/electrical, fan vents, and those in corners. Unless sealed, you'll lose heating and waste money. If the previous fiberglass batts had dark marks, they generally indicate an air leak. You can lay insulation batts in the directions you mentioned, but I'd go with the most effective insulation at the lowest cost. If your attic has an access panel, insure you've built a "surround" and tightly sealing door, as well.